Something like:
Create a hash for the image on the server and put that hash in a page on the server that can be accessed. Anytime the picture changes on the server, update the hash.
On the client, if you download the picture for the first time, download it and create a hash (using same hashing function) of the picture. Later on, before displaying the picture on the client, request the page on the server that has the hash and compare it to your client hash. If it is not the same has, download the picture, otherwise just display the local copy of the picture.
This would probably only be worth it if the picture is of some significant size or download speeds are abysmally slow (or combo).